Question

A collection of quarters and dimes is worth $12.40. There are 67 coins in all.

Answer 1

Let:
x= quarters
y= dimes


x+y=67
and
.25x+.10y=12.40

x=67-y

.25(67-y)+.10y=12.40
16.75-.25y+10y=12.40
16.75-.15y=12.40
Lets rearrange this:
-.15y+16.75=12.40
        -16.75    -16.75
-.15y=-4.35
the negatives cancel out
.15y=4.35
.15     .15
y=29

Back to the original x=67-y
x=67-29
x=38

So,
x=38
y=29